Journal
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
Volume 54, Issue 5, Pages 690-697Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ijar.2013.01.007
Keywords
Formal context; Concept lattice; Generalized concept system; Set-theoretic operator; Dual operator
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Funding
- National Natural Science Foundation of China [10901025]
- Special Fund for Basic Scientific Research of Central Colleges [CHD2012JC003]
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Formal concept analysis is an algebraic model based on a Galois connection. It is used for symbolic knowledge exploration from an elementary form of a formal context. This paper mainly presents a general framework for concept lattice in which axiomatic approaches are used. The relationship between concept lattice and dual concept lattice is first studied. Based on set-theoretic operators, generalized concept systems are established. And properties of them are examined. By using axiomatic approaches, a pair of dual concept lattices is characterized by different sets of axioms. The connections between 0-1 binary relations and generalized concept systems are examined. And generalized dual concept systems can be constructed by a pair of dual set-theoretic operators. Axiomatic characterizations of the generalized concept systems guarantee the existence of a binary relation producing a formal context. (C) 2013 Elsevier Inc. All rights reserved.
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